Mr. Clean magic eraser. And I would advise taking an extra english class.
Magic Erasers are GREAT, but do rub the marks GENTLY because the eraser might erase your paint as well! Usually they won't take away the paint but can leave a lightly sanded look to glossy finishes. And another warning here about Magic Eraser sponges: THEY ARE HIGHLY ADDICTIVE! :) You'll be scrubbing floors, tile, outside toys and furniture, inside of aquariums, stoves, inside of fridge (I won't clean a fridge without a Magic Eraser anymore), upholstery in your car....etc, etc, etc You'll become hooked - I promise! My daughter says I should be their spokesperson! :D
Try wood alcohol (I used it to get sharpie off a fridge, a whiteboard and a window)
You can get wood alcohol at auto parts stores or truck stops, it's sold as air break antifreeze for trucks.
plain ol' rubbing alcohol will act as a fine solvent for that type of ink, too
if its permenant marker - use a WHITEBOARD marker (dry-erase) and rub the markings. Dry erase wont come off either, but it will dissolve permanent ink. Then use white-board cleaner to remove the dry erase.
I wouldn't recommend goof-off, because it might dissolve and melt the marker into the fridge enamel. I had to do this before - worked like a charm. Also try mr clean magic erasers.
There's a solvent called Goof Off that I'd try
Bleach or hydrogen peroxide might 'bleach' the marker-ink so that it is less/in-visible. Try this on a bit of the fridge that is usually hidden from view first, to check that it doesn't have an adverse effect on the textured finish.